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$(22)$ Consider the par yield curve for the U$.$S$.$ Treasury securities given in the table below $($only the first $3$ years, or $6$ semiannual periods, of the curve are provided$).$ Calculate the missing spot rates for years $1\mathrm{.}5,2\mathrm{.}0,2\mathrm{.}5$ and $3\mathrm{.}0$ using bootstrapping and add them to the table. Remember that all interest rates are quoted on an annual basis and may have to be converted to or from a semiannual rate. Show your work for all calculations in the space below the table

$\backslash$table$[[$Year$,$Yield to Maturity $(\%),$Spot Rate $(\%)],[0\mathrm{.}5,5\mathrm{.}25,5\mathrm{.}25,,,],[1\mathrm{.}0,5\mathrm{.}50,5\mathrm{.}50,,,],[1\mathrm{.}5,5\mathrm{.}75,,,,],[2\mathrm{.}0,6\mathrm{.}00,,,,],[2\mathrm{.}5,6\mathrm{.}25,,,,]]$